Pseudo Random Distribution

From Liquipedia Dota 2 Wiki

As chance would have it.

Pseudo Random Distribution (shortened PRD) is a mechanic ported to Dota 2 which originated from the Warcraft 3 engine. Pseudo-random distributions are used to calculate chance based skills including critical strike, bash, and evasion abilities.
In more common random distributions, every possible check has the same chance of activation regardless of any prior checks.
In pseudo-random distribution streaks of activation or streaks of no activation are less likely, but the overall probability remains the same.

The PRD works by increasing the percentage chance for an activation by a certain amount every time it didnt activate until the chance for activation is over 100%.
On the other side right after an activation the chance for another activation is significantly lower than the chance stated in the skill/item description.
This means that skills such as critical strike will occur more consistently than they would in more common standard random distributions. Significantly streaks of "good luck" or "bad luck" are less likely to occur, making the game less luck dependent.

The base and incremental chances were precalculated and accessed from table because the calculations needed to produce those chances for each probability under PRD are taking up much more processor runtime than those for the same probability under standard random distribution. The values in Warcraft 3 were in 5% steps and, curiously, incorrect for chances of 15% and higher. These errors increase for each step and become noteworthy from 35% onward.
It is assumed that these errors were ported over to Dota 2 for parity reasons.

The chance for an activation on first hit/check is also the amount by which the chance is incremented each time no activation occurs. The chance will not increase by an event in which an activation cannot occur. This makes abusing the PRD difficult, because, for example, hitting a building will not increase the chance of a critical strike, because you critical strike do not work against buildings in the first place.

In the following table, P(E) is the probability that the PRD is trying to mimic. Theoretical C is the value the PRD table should use to result in the correct probability. Actual C is the value used by the Warcraft 3 engine (and presumably Dota 2), resulting in a skewed probability. Max N is the number of attacks after which the chance for an activation(C*N) reaches 100%. P(A) is the actual probability of an activation occurring.

P(E)

Theoretical C

Actual C

Theoretical Max N

Actual Max N

P(A)

5%

0.00380

0.00380

263

263

5.0%

10%

0.01475

0.01475

67

67

10.0%

15%

0.03222

0.03221

31

31

15.0%

20%

0.05570

0.05570

17

17

20.0%

25%

0.08474

0.08475

11

11

24.9%

30%

0.11895

0.11895

8

8

29.9%

35%

0.15798

0.14628

6

6

33.6%

40%

0.20155

0.18128

4

5

37.7%

45%

0.24931

0.21867

4

4

41.8%

50%

0.30210

0.25701

3

3

45.7%

55%

0.36040

0.29509

2

3

49.3%

60%

0.42265

0.33324

2

3

53.0%

65%

0.48113

0.38109

2

2

56.6%

70%

0.57143

0.42448

1

2

60.1%

The following graphics show how the distribution for a 15% chance differ between PRD and standard random distribution.